A sparse overview on sparse resultants

Abstract: In this survey, we give an overview of advances in the theory and computation of sparse resultants. First, we examine the construction and proof of the Canny-Emiris formula, which gives a rational determinantal formula. Second, we discuss and compare the latter with the computation of the sparse resultant as the determinant of the Koszul complex given by $n + 1$ nef divisors in a toric variety. Finally, we cover techniques for computing the Newton polytope of sparse resultants.